Linear Law - Predictions from Linearised Models
Linear Law - Predictions from Linearised Models
A stone is thrown from point \(P\) on top of a cliff. As it travels through the air, it follows a curved path, reaching a maximum height at point \(Q\) before falling into the sea. The table below shows the height \(y\) (in metres) of the stone at various horizontal distances \(x\) (in metres) from the point it was thrown:
| \(x\) | \(1\) | \(2\) | \(4\) | \(6\) | \(8\) | \(10\) | \(12\) |
|---|---|---|---|---|---|---|---|
| \(y\) | \(7\) | \(16\) | \(24\) | \(24\) | \(16\) | \(0\) | \(-24\) |
It is given that \(x\) and \(y\) are related by the equation \(y = mx^2 + nx\), where \(m\) and \(n\) are constants.
Use this information to:
- draw the straight-line graph of \(\frac{y}{x}\) against \(x\) and estimate the values of \(m\) and \(n\).
- determine which value of \(y\) is incorrect and estimate its correct value.
- estimate the horizontal distance from the cliff when the stone is at point \(R\).
- estimate the maximum height reached by the stone.
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